Learning to Optimize: Joint Routing and Flow Allocation on Sparse Non-Euclidean Networks

• URL: http://arxiv.org/abs/2607.23467v1
• Date: Sun, 26 Jul 2026 05:30:27 GMT
• Title: Learning to Optimize: Joint Routing and Flow Allocation on Sparse Non-Euclidean Networks
• Abstract summary: We study an integrated pickup-and-delivery problem on sparse, non-Euclidean networks.<n>We propose Double-Channel Graph Attention (DCGA), an end-to-end reinforcement learning framework.
• Score: 4.631384046993308
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study an integrated pickup-and-delivery problem on sparse, non-Euclidean networks that jointly optimizes cyclic routing, cargo flow allocation, and cross-cycle service. The tight coupling of these operational constraints creates a complex discrete-continuous decision space with highly restricted feasible regions. To overcome these computational challenges, we propose Double-Channel Graph Attention (DCGA), an end-to-end reinforcement learning framework. DCGA isolates network reachability and demand-service logic into separate graph channels and constructs valid routes using a simulator-coupled, constraint-informed decoder. Experiments on LinerLib benchmarks demonstrate that DCGA achieves seconds-level inference and delivers state-of-the-art solution quality on instances beyond a specific scale, with its advantage over existing baselines widening significantly as problem size increases. Supported by extensive stability and ablation analyses, our results demonstrate that this structure-aware learning approach provides an effective, low-latency engine for realistic routing-and-flow optimization.

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